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Simplifying abs(3x + -2) = abs(5x + -4) Reorder the terms: abs(-2 + 3x) = abs(5x + -4) (-2 * abs + 3x * abs) = abs(5x + -4) (-2abs + 3absx) = abs(5x + -4) Reorder the terms: -2abs + 3absx = abs(-4 + 5x) -2abs + 3absx = (-4 * abs + 5x * abs) -2abs + 3absx = (-4abs + 5absx) Solving -2abs + 3absx = -4abs + 5absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4abs' to each side of the equation. -2abs + 4abs + 3absx = -4abs + 4abs + 5absx Combine like terms: -2abs + 4abs = 2abs 2abs + 3absx = -4abs + 4abs + 5absx Combine like terms: -4abs + 4abs = 0 2abs + 3absx = 0 + 5absx 2abs + 3absx = 5absx Add '-5absx' to each side of the equation. 2abs + 3absx + -5absx = 5absx + -5absx Combine like terms: 3absx + -5absx = -2absx 2abs + -2absx = 5absx + -5absx Combine like terms: 5absx + -5absx = 0 2abs + -2absx = 0 Factor out the Greatest Common Factor (GCF), '2abs'. 2abs(1 + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve: Simplifying abs = 0 Solving abs = 0 Move all terms containing a to the left, all other terms to the right. Simplifying abs = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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